A four$-$pole Y$-$connected synchronous generator rated at $30$kVA,$380V,50Hz,$ and $0\mathrm{.}9$ PF lagging. Its armature resistance $R_A$ is $0\mathrm{.}02$ and its synchronous reactance $x_s$ is $0\mathrm{.}95.$ The core losses of this generator at rated conditions are $0\mathrm{.}5$ kW $,$ and the friction and windage losses are $0\mathrm{.}4$ kW $.$

a$.$ What are the rated current $I_A$ and internal generated voltage $E_A$ of this generator, draw the phasor diagram?

b$.$ For point $($a$)$ compute the reactive power and show if it is consumed or delivered to the load,

c$.$ What is the voltage regulation of this generator at the rated current and power factor? Is this good or not and why?

d$.$ If this generator is operating at the rated conditions and the load is suddenly removed, what will the terminal voltage be$?$ What will happen to the active and reactive power? Draw the phasor diagram for this operating point?